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Jewish Calendar Accuracy

77% of the holy days in the past 100 years have been on the wrong date according to the Jewish calendar when taking into account the accumulated seasonal drift caused by inaccurate math calculations and the changing rate of movement of the earth and moon. (Test this yourself) The seemingly small math differences expressed in a number of writings on the subject of the accuracy of the Jewish calendar may be causing people to assume that the Jewish calendar can accurately express when God's holy days are. But a small error in one calculation can lead to much larger errors when multiplied many times over.

The following quote is used in a number of Church of God articles [1] to espouse the accuracy of the Jewish calendar. This is despite the fact that the quote clearly states there is an error in the Jewish calendar.

The calculation of the calendar was transmitted to the sages in an unbroken chain going back to Moses. … According to the ancient calculations, the exact time between one new moon and the next is 29 days, 12 hours, and 793 chalakim ‘parts of an hour’ (the hour is divided into 1080 parts). In other words, one lunar month has 29.53059 days. It is interesting to note that according to NASA (National Aeronautics and Space Administration); the time between one new moon and the next is 29.530588 days. Of course, NASA has at its disposal the most advanced and sophisticated telescopes and computers. Nevertheless, the difference between NASA’s figures and that used by Hillel II, which originated more than 3000 years ago, is .000002 or two millionths of a day, calculated for the period of one month. The Essence of the Holy Days: Insights from the Jewish Sages by Avraham Yaakov Finkel, 1993, p. 141

According to Finkel the error of the Jewish calendar is only 2 millionths of a day, which translates into -.17 seconds per month. This would mean that the Jewish calendar gave the wrong dates 23% of the time in the last 100 years. (Test this yourself) But Finkel's number "2 millionths of a day", or -.17 seconds, itself is inaccurate and quoting Finkel is spreading misinformation about the accuracy of the Jewish calendar.

How accurate is the Hebrew calendar?

According to Judaism 101, the average lunar month on the Hebrew calendar and the average lunar month calculated by modern astronomers are only different by “about half of a second. That is quite remarkably accurate.”

COGWA Young Adult Blog, Leap Day, Leap Months and Other Notable Times

How accurate is the Jewish calendar actually?

About "half a second" (-.5 seconds) and "2 millionths of a day" (-.17 seconds) seem like insignificant differences until you realize this difference is multiplied 10s of thousands of times. For the year 2018 this error is multiplied 71,440 times.

Also, there is a 66% difference between -.5 seconds and -.17, which is a significant amount, so which is more accurate? Can tiny fractions of a second really make any difference when calculating the dates for the holy days? (Test this yourself)

Dr. Irv Bromberg, an expert in the math of the Jewish calendar, and the Sanhedrein's source for the math of the Jewish calendar says this.

The Mean Synodic Month is currently about 3/5 second or 9/50 of a part [3 1/3 seconds] shorter than the traditional molad interval... Dr. Irv Bromberg, Moon and the Molad of the Hebrew Calendar

3/5 of a second difference is -.6 seconds. But a more accurate formula from Dr. Irv Bromberg shows that the value is closer to -.57 seconds.

Traditional Molad Period = 29 days 12 hours 793 parts = 29 days 12 hours 44 minutes 1 part = 29.53059414 days.
...
Apparent Mean Synodic Month at present = 29.53058751 solar days = 0.57 seconds shorter than Molad period.

Dr. Irv Bromberg, Apparent Mean Synodic Month vs. Lunation

In addition to this disparity months are becoming shorter every year. This means the accuracy of the molad, and therefore the accuracy of the Jewish calendar, is degrading more as time passes.

Can these seemingly minute difference really matter all that much? We can test this ourselves using the app below.

Test it yourself

The most accurate difference is -.57 seconds. The approximate value of 3/5 of second is -.6 seconds. 2 Millionths of a month is -.17 seconds. How much of a difference do any of these make in calculating the dates of the holy days using the Jewish calendar?

Molad difference (in seconds)
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From year: BCE to BCE ({{total_years}} years)

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Holy Day Errors: {{errors_percentage}}%
Total on wrong date: {{i_errors}}
Off by 1 day: {{errors_off_by_1}}
Off by 2 days: {{errors_off_by_2}}
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Error
(days diff.)
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(Jewish Molad)
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References